Question

Exercise 3.5 Calculate the number of carbon atoms in 20.0 g of propane, C3H8. 3(12.01)

Answer 1

Propane is C₃H₈

1 mole of propane has 3 carbon atoms and 8 hydrogen atoms.

1 mole of any substance has the Avogadro number 6.022 ×10²³ particles/mol

Given mass = 20 grams

Molar mass is the sum of the atomic masses of all atoms present in the molecule:

So for propane:

Each Carbon atom has an atomic mass = 12 g / mol

Each Hydrogen atom has a atomic mass = 1 g / mol

So the molar mass of propane is (3 × 12) + (8× 1) = 44 g / mol

The percentage of Carbon in 1 mole of propane = (3 × 12) ×100 / 44 = 81.8%

Then the mass of carbon in 20 grams of propane = (81.8 × 20) / 100 = 16.36 g

Now 16.36 grams of Carbon corresponds to how many moles of Carbon

Number of moles = Available mass / Molar mass

Number of moles of carbon = 16.36 / 12 = 1.3633 moles

The number of atoms in any substance is defined as number of moles of that substance × Avogadro’s constant

So the number of carbon atoms in 20 grams of propane = 1.3633 mol ×6.022 × 10²³ atoms / mol = 8.207 × 10²³ atoms

Hence the number of carbon atoms in 20 grams of propane is 8.207 × 10²³